## Topological Methods in Nonlinear Analysis

### Multiplicity of solutions of some quasilinear equations in ${\mathbb{R}^{N}}$ with variable exponents and concave-convex nonlinearities

#### Abstract

We prove multiplicity of solutions for a class of quasilinear problems in $\mathbb{R}^{N}$ involving variable exponents and nonlinearities of concave-convex type. The main tools used are variational methods, more precisely, Ekeland's variational principle and Nehari manifolds.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 2 (2016), 529-559.

Dates
First available in Project Euclid: 13 July 2016

https://projecteuclid.org/euclid.tmna/1468413751

Digital Object Identifier
doi:10.12775/TMNA.2016.015

Mathematical Reviews number (MathSciNet)
MR3559919

Zentralblatt MATH identifier
1365.35044

#### Citation

Alves, Claudianor O.; Barreiro, José L. P.; Gonçalves, José V. A. Multiplicity of solutions of some quasilinear equations in ${\mathbb{R}^{N}}$ with variable exponents and concave-convex nonlinearities. Topol. Methods Nonlinear Anal. 47 (2016), no. 2, 529--559. doi:10.12775/TMNA.2016.015. https://projecteuclid.org/euclid.tmna/1468413751

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